How about 'Unseen Narratives' or 'Cloaked Chronicles'?
'Secret Chronicles', 'Hidden Tales', 'Personal Reveries' are great creative names for private stories.
How about 'The Veiled Verses'? The word 'veiled' gives a sense of something being covered or hidden, just like a private story. And 'verses' can be associated with stories or tales. 'The Forbidden Folios' could also work. 'Folios' are like pages of a book, and 'forbidden' adds an element of secrecy and privacy. 'The Clandestine Chronicles' is another good one. 'Clandestine' means secret or stealthy, which suits a private story well.
Private Moments Gallery. This name gives the idea that your snap story is a collection of personal and private moments that are precious to you. It has a bit of an artistic and exclusive feel to it.
You can use 'The Jolly Jumbles' or 'The Wacky Wonders'.
Creative names for fitness private stories can come from your emotions during fitness. If you feel empowered, 'Empowered Fitness: My Story'. You could also use a play on words. For example, if you do a lot of running, 'Running Ruminations: My Fitness Narrative'. Additionally, naming it based on the season you started your fitness journey can be interesting. So, if it was in spring, 'Spring into Fitness: My Personal Tale' would be a good choice.
How about 'My Mysterious Musings', 'Sneaky Snaps' or 'Covert Craziness'?
How about 'Exclusive Exposures'? It makes it seem like the story reveals things that only a select few can see. Or 'Confidential Chronicles' which emphasizes the secrecy and personal nature of the story.
How about 'My Secret Sanctuary'? It gives the feeling that the story is a safe and private place.